Inverse Trig. Functionsand Differentiation

Inverse Trig. Functionsand Differentiation - domains...

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Inverse Trig. Functions & Differentiation Section 5.6
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Inverse Trig. Functions None of the 6 basic trig. functions has an inverse unless you restrict their domains. Look at chart on pg. 377.
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Function Domain Range y = arcsin x -1< x < 1 I & IV y = arccos x -1< x < 1 I & II y = arctan x - < x < I & IV y= arccot x - < x < I & I y = arcsec x I & II y = arccsc I & IV 1 x 1 x
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Inverse Properties f (f –1 (x)) = x and f –1 (f (x)) = x Remember that the trig. functions have inverses only in restricted
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Unformatted text preview: domains. Derivatives of Inverse Trig. Functions Let u be a differentiable function of x. [ ] 2 ' 1 arcsin u u u dx d-= [ ] 2 ' 1 arccos u u u dx d--= [ ] 2 ' 1 arctan u u u dx d + = [ ] 2 ' 1 cot u u u arc dx d +-= [ ] 1 sec 2 '-= u u u u arc dx d [ ] 1 csc 2 '--= u u u u arc dx d Joke Time Who stole the soap? The Robber Ducky! What do you call 2 spiders who just got married? Newlywebs...
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